Approximate pricing formula to capture leverage effect and stochastic volatility of a financial asset

In this paper a hybrid model is investigated to capture both financial behaviors of an asset: (i) the leverage effect and (ii) the stochastic volatility component. For this we consider a hybrid model that takes the strengths of the Heston and the CEV models. The pricing of European options is investigated both theoretically and empirically. A decomposition formula that allows to estimate the option price is obtained. Moreover, numerical simulations of the asset price are done to give a better and concrete vision of the adding of this approach. In addition, the price of a European call option under the hybrid model is computed using the Monte Carlo method and our formula. Illustrations and tables show the efficiency of the numerical method based on our approximate formula